The approximation of the solutions of equations using approximant sequences
Adrian Diaconu · Journal of Numerical Analysis and Approximation Theory · 2003
We intend to characterize the convergence of a certain sequence that belongs to a subset of a Banach space towards the solution of an equation obtained by the annulment of a nonlinear mapping that is defined on this subset and that takes values in another linear normed space. This mapping has a Fréchet derivative of a certain order which verifies the Lipschitz condition. We can establish some conditions that are enough both for the existence of the equation's solution and for a speed of convergence of a certain order for the approximant sequence.